Using excel to implement the finite difference method for 2-D heat transfer in a mechanical engineering technology course

Abstract

Multi-dimensional heat transfer problems can be approached in a number of ways. Sometimes an analytical approach using the Laplace equation to describe the problem can be used. This involves finding the solution of differential equations, which may be reasonable for Mechanical Engineering Technology (MET) students. However, these students are not always particularly proficient in using this approach. Also, the analysis can get quite complex depending on boundary conditions, often involving advanced mathematics using Bessel functions, Fourier series and other special functions. Graphical methods might be used, but their usefulness extends primarily to discussions about the relationships between isotherms and heat flow paths. Shape factors and other approximations can also be useful in certain instances. None of these seem to provide an especially good approach for MET students. A more practical approach for these students is the use of numerical methods. The finite difference method seems to provide a good approach for MET students. Using this method a student can model fairly complex two-dimensional problems with a variety of boundary conditions using a simple spreadsheet. This paper presents information on how this method is used at Penn State Erie, The Behrend College in a first course in heat transfer for MET students. The method is used to aid in presenting the theory, as well as for a laboratory exercise. The basic equations for a variety of node types are included, as well as equation modifications that are used to account for several thermal loading and boundary conditions. The lectures are reinforced with homework practice problems before the more involved lab exercise. Finally, the lab exercise is included. The exercise is designed to give the students practice using the method. © American Society for Engineering Education, 2014.